Experimental studies have shown that convergent–divergent nozzles, when run at low
pressure ratios, often undergo a flow resonance accompanied by emission of acoustic
tones. The phenomenon, different in characteristics from conventional ‘screech’ tones,
is addressed in this paper. Unlike screech, the resonant frequency (fN) increases
with increasing supply pressure. There is a ‘staging’ behaviour; odd-harmonic stages
resonate at lower pressures while the fundamental occurs in a wide range of higher
pressures corresponding to a ‘fully expanded Mach number’ (Mj) around unity. Within
a stage, fN varies approximately linearly with Mj; the slope of the variation steepens
when the angle of divergence of the nozzle is decreased. Based on the data, correlation
equations are provided for the prediction of fN. A companion computational study
captures the phenomenon and predicts the frequencies, including the stage jump,
quite well. While the underlying mechanisms are not completely understood yet, it is
clear that the unsteadiness of a shock occurring within the divergent section plays
a direct role. The shock drives the flow downstream like a vibrating diaphragm,
and resonance takes place similarly to the (no-flow) acoustic resonance of a conical
section having one end closed and the other end open. Thus, the fundamental is
accompanied by a standing one-quarter wave within the divergent section, the next
stage by a standing three-quarter wave, and so on. The distance from the foot of the
shock to the nozzle exit imposes the pertinent length scale. The principal trends in
the frequency variation are explained qualitatively from the characteristic variation of
that length scale. A striking feature is that tripping of the nozzle's internal boundary
layer tends to suppress the resonance. It is likely that the trip effect occurs due to a
break in the azimuthal coherence of the unsteady flow.
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